Average Error: 0.1 → 0.1
Time: 16.6s
Precision: 64
\[\left(x + \sin y\right) + z \cdot \cos y\]
↓
\[\mathsf{fma}\left(\cos y, z, x + \sin y\right)\]
\left(x + \sin y\right) + z \cdot \cos y
↓
\mathsf{fma}\left(\cos y, z, x + \sin y\right)
double f(double x, double y, double z) {
        double r135254 = x;
        double r135255 = y;
        double r135256 = sin(r135255);
        double r135257 = r135254 + r135256;
        double r135258 = z;
        double r135259 = cos(r135255);
        double r135260 = r135258 * r135259;
        double r135261 = r135257 + r135260;
        return r135261;
}
↓
double f(double x, double y, double z) {
        double r135262 = y;
        double r135263 = cos(r135262);
        double r135264 = z;
        double r135265 = x;
        double r135266 = sin(r135262);
        double r135267 = r135265 + r135266;
        double r135268 = fma(r135263, r135264, r135267);
        return r135268;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

    \[\left(x + \sin y\right) + z \cdot \cos y\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, x + \sin y\right)}\]

  3. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(\cos y, z, x + \sin y\right)\]

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C"
  (+ (+ x (sin y)) (* z (cos y))))